Both advanced to the semi-finals of the clay-court tournament on Friday and could repeat last weekend's Argentina Open decider, which the Spaniard won.
Defending Rio Open champion Alcaraz beat Dusan Lajovic 6-4 7-6 (7-0).
He will now meet Nicolas Jarry, who accounted for Sebastian Baez 6-3 7-6 (7-3).
Once again, the 19-year-old Alcaraz did not play his best tennis in Brazil as in his first two matches, but still prevailed.
Unforced errors, difficulties with his first serve and less energy than the usual were evident throughout the Spaniard's match against Lajovic.
Alcaraz, who won last year's US Open for his first major, is playing his second tournament since a right leg injury that sidelined him for four months.
Alcaraz and Jarry have never played each other in a tour match.
"I feel I am at a great level physically, I am playing tough, demanding matches day after day," Alcaraz said.
"Last year I was at a great level, winning here, Miami, other tournaments. I can still improve what I am doing now, obviously."
Second-seeded Norrie overcame Bolivia's Hugo Dellien 4-6 6-1 6-4. The British player will next take on Bernabe Zapata Miralles, who beat Spanish compatriot Albert Ramos-Vinolas 6-4 2-6 6-4.
"I had a very slow start, I didn't make a lot of returns, which is pretty unlike me," Norrie said. "I was fortunate to stay patient."
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